量子轨道的事件力学：连续测量、量子预言和反馈控制
Eventum Mechanics of Quantum Trajectories: Continual Measurements, Quantum Predictions and Feedback Control
摘要：
量子力学系统在测量时表现出固有的概率性质，这在原则上排除了奇异的直接可观测性连续的情况。80年代，作者在量子噪声的独立增量模型和非破坏因果原理的基础上发展起来的时间连续测量量子理论和量子预测理论，解决了这个问题，允许连续量子预测，并将许多量子信息问题，如量子反馈控制问题，归结为经典的随机问题。利用扩散和计数测量的显式间接观测模型，导出了描述开放量子系统在连续部分观测下随机演化的量子滤波（预测）方程.与经典的不确定性控制理论并行工作，我们给出了以这两种测量为条件的后验随机量子态的最优反馈控制的Markov Bellman方程.由此产生的过滤和贝尔曼方程的扩散观测，然后应用到显式可解的量子线性二次高斯（LQG）问题，强调了许多相似之处和不同之处，相应的经典非线性滤波和控制问题，并证明量子滤波和经典控制之间的微观对偶。
英文摘要：
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement which excludes in principle the singular direct observability continual case. Quantum theory of time continuous measurements and quantum prediction theory, developed by the author on the basis of an independent-increment model for quantum noise and nondemolition causality principle in the 80's, solves this problem allowing continual quantum predictions and reducing many quantum information problems like problems of quantum feedback control to the classical stochastic ones. Using explicit indirect observation models for diffusive and counting measurements we derive quantum filtering (prediction) equations to describe the stochastic evolution of the open quantum system under the continuous partial observation. Working in parallel with classical indeterministic control theory, we show the Markov Bellman equations for optimal feedback control of the a posteriori stochastic quantum states conditioned upon these two kinds of measurements. The resulting filtering and Bellman equation for the diffusive observation is then applied to the explicitly solvable quantum linear-quadratic-Gaussian (LQG) problem which emphasizes many similarities and differences with the corresponding classical nonlinear filtering and control problems and demonstrates microduality between quantum filtering and classical control.
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